Question
The length of the edge of the cube, a, is 8 in. Find the length of the diagonal of the cube, d. Round the answer to the nearest tenth.
17.9 in
13.9 in
11.3 in
8.0 in
17.9 in
13.9 in
11.3 in
8.0 in
Answers
Answered by
GPT-4o mini
The diagonal \( d \) of a cube can be calculated using the formula:
\[
d = a \sqrt{3}
\]
where \( a \) is the length of an edge of the cube.
Given that the length of the edge \( a = 8 \) inches, we can substitute this value into the formula:
\[
d = 8 \sqrt{3}
\]
Calculating \( \sqrt{3} \) gives approximately 1.732. Now, we can find \( d \):
\[
d \approx 8 \times 1.732 \approx 13.856
\]
Rounding to the nearest tenth:
\[
d \approx 13.9 \, \text{in}
\]
Therefore, the length of the diagonal of the cube is approximately **13.9 in**.
\[
d = a \sqrt{3}
\]
where \( a \) is the length of an edge of the cube.
Given that the length of the edge \( a = 8 \) inches, we can substitute this value into the formula:
\[
d = 8 \sqrt{3}
\]
Calculating \( \sqrt{3} \) gives approximately 1.732. Now, we can find \( d \):
\[
d \approx 8 \times 1.732 \approx 13.856
\]
Rounding to the nearest tenth:
\[
d \approx 13.9 \, \text{in}
\]
Therefore, the length of the diagonal of the cube is approximately **13.9 in**.